A radioactive substance is decaying at a rate of 5 percent per day. This means that every day it looses 5 percent of its total weight. The substance starts with a weight of 80 grams. What equation can represent the decay of the substance?(1 point)

f (x)=80(1.05)^x-1
f (x)= 80(0.995)^x-1
f (x) 80(0.95)^x-1
f (x)= 80(0.5)^x-1

1 answer

To represent the decay of a radioactive substance that loses 5% of its total weight per day, you can use the exponential decay formula:

\[ f(x) = f_0 \cdot (1 - r)^x \]

where:

  • \( f_0 \) is the initial weight (80 grams in this case),
  • \( r \) is the decay rate (5% or 0.05),
  • \( x \) is the number of days.

Since it loses 5%, the fraction remaining after one day is \( 1 - 0.05 = 0.95 \).

Therefore, the equation becomes:

\[ f(x) = 80 \cdot (0.95)^x \]

However, in the provided options, the equations all have a "-1" at the end, which is not appropriate for the decay function in this context.

Thus, if we only focus on finding the decay equation itself without the "-1", the correct choice would be:

f(x) = 80(0.95)^x

Since the provided options include an irrelevant "-1", none of the given options accurately represent the decay equation. If we consider just the functioning part without the "-1", we can conclude that:

The correct decay function is:

f(x) = 80(0.95)^x (not in your options).